Abstract

An achromatic infrared (λ=1.24 μm), Si-prism quarter-wave retarder (QWR) is described that uses total internal reflection at a buried SiSiO2 interface at an angle of incidence ϕ near 33°, where Δ/ϕ=0. The retardance Δ deviates from 90° by <±2° within a field of view of ±10° (in air) over the entire bandwidth. Because the SiO2 layer at the base of the prism is optically thick, this QWR is unaffected by environmental contamination.

© 2004 Optical Society of America

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References

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  2. D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).
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    [Crossref]
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  16. I. Filinski, T. Skettrup, “Achromatic phase retarders constructed from right-angle prisms: design,” Appl. Opt. 23, 2747–2751 (1984).
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  17. Technical Sessions “Optical Silicon I & II,” Conference program, 2002 OSA Annual Meeting, September 29-October 3, 2002, Orlando, Fla.
  18. R. M. A. Azzam, M. M. K. Howlader, “Silicon-based polarization optics for the 1.30- and 1.55-μm communication wavelengths,” J. Lightwave Technol. 14, 873–878 (1996).
    [Crossref]
  19. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
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  21. W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. II, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Chap. 33.
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2004 (1)

2003 (2)

2002 (1)

2001 (2)

1998 (1)

1996 (1)

R. M. A. Azzam, M. M. K. Howlader, “Silicon-based polarization optics for the 1.30- and 1.55-μm communication wavelengths,” J. Lightwave Technol. 14, 873–878 (1996).
[Crossref]

1995 (1)

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–875 (1995).
[Crossref]

1986 (1)

S. Zhu, A. W. Yu, D. Hawley, R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

1985 (1)

1984 (2)

1983 (1)

1982 (1)

1980 (1)

1970 (1)

Apfel, J. H.

Azzam, R. M. A.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Bennett, J. M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Boulbry, B.

Bousquet, B.

Case, S. K.

Chia, R. Y.

Clarke, D.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

Craighead, H. G.

De, A.

Enger, R. C.

Filinski, I.

Grainger, J. F.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

Guern, Y.

Harris, T. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. II, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Chap. 33.

Hawley, D.

S. Zhu, A. W. Yu, D. Hawley, R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

Hickmann, J. M.

Howlader, M. M. K.

R. M. A. Azzam, M. M. K. Howlader, “Silicon-based polarization optics for the 1.30- and 1.55-μm communication wavelengths,” J. Lightwave Technol. 14, 873–878 (1996).
[Crossref]

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–875 (1995).
[Crossref]

Javily, K.

Le Jeune, B.

Lopez, A. G.

Lotrian, J.

Mahmoud, F. A.

McCormick, C. F.

Röseler, A.

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990).

Roy, R.

S. Zhu, A. W. Yu, D. Hawley, R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard University Press, Cambridge, Mass., 1962).

Skettrup, T.

Solli, D. R.

Southwell, W. H.

Spiller, E.

Thomas, M. E.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. II, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Chap. 33.

Tropf, W. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. II, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Chap. 33.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yu, A. W.

S. Zhu, A. W. Yu, D. Hawley, R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

Zhu, S.

S. Zhu, A. W. Yu, D. Hawley, R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

Am. J. Phys. (1)

S. Zhu, A. W. Yu, D. Hawley, R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

Appl. Opt. (8)

J. Lightwave Technol. (1)

R. M. A. Azzam, M. M. K. Howlader, “Silicon-based polarization optics for the 1.30- and 1.55-μm communication wavelengths,” J. Lightwave Technol. 14, 873–878 (1996).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–875 (1995).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Other (7)

W. A. Shurcliff, Polarized Light (Harvard University Press, Cambridge, Mass., 1962).

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Technical Sessions “Optical Silicon I & II,” Conference program, 2002 OSA Annual Meeting, September 29-October 3, 2002, Orlando, Fla.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. II, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Chap. 33.

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990).

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Figures (6)

Fig. 1
Fig. 1

QWR that uses total internal reflection at the base of a Si prism and that is coated with an optically thick SiO2 film. The entrance and exit faces are antireflection coated. The optimum operating angle is ϕ=32.765°.

Fig. 2
Fig. 2

Plot of Δ versus ϕ [by use of Eq. (1)] for n=2+1 confirms the conditions represented by Eqs. (3) and (4).

Fig. 3
Fig. 3

Refractive indices of Si and SiO2 [given by Eqs. (5) and (6)] are plotted as functions of wavelength λ.

Fig. 4
Fig. 4

Relative refractive index n=n(Si)/n(SiO2) [calculated by using Eqs. (5) and (6)] is plotted as a function of wavelength λ. Note that n=2+1 at λ1=1.4224 μm, λ2=2.8644 μm.

Fig. 5
Fig. 5

Retardance Δ versus λ for TIR at the SiSiO2 interface at five angles in the neighborhood of ϕ=32.765°.

Fig. 6
Fig. 6

Contours of constant Δ in the λ–ϕ parameter space, where Δ takes values between 88° and 91° in steps of 0.5°. This nomogram is constructed based on Eqs. (1) and (5)–(7).

Equations (9)

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tan(Δ/2)=(n2sin2 ϕ-1)1/2/(n sin ϕ tan ϕ),
n=n0/n1
Δ=90°,Δ/ϕ=0,
n=2+1=2.414214,
ϕ=ϕ90=arccos(2-1/4)=32.7651°.
n2(Si)=1+10.6684293λ2λ2-(0.301516485)2+0.003043475λ2λ2-(1.13475115)2+1.54133408λ2λ2-(1104.0)2,
n2(SiO2)=1+0.6961663λ2λ2-(0.0684043)2+0.4079426λ2λ2-(0.1162414)2+0.8974794λ2λ2-(9.896161)2.
n=n(Si)/n(SiO2),
λ1=1.4224μm,λ2=2.8644μm.

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